How to measure the voltage on the VDG? You can't connect a meter,
since anything touching the sphere causes discharges. The breakdown
voltage in air depends on many things, including the shape of the grounded
object. I had observed that my discharge sphere
(B on this picture) moves every time there
is a spark, which means there is a noticable force that attracts it to the
VDG dome when it is charged up.
Based on that, I built the contraption shown on the right. The grounded sphere is suspended from one arm of a sensitive balance, and a counterweight is suspended from the other end. The counterweight is a can filled with enough screws to balance the sphere, plus a few (Order 10g) grams more. The can rests on my electronic kitchen scale. In the picture, I have highlighted the (thin, non-stretch) string that runs up from the sphere, over two small nails on the balance arm, and down to the can, where it is tied with a simple knot. | |
The balance is an inverted V, where the fulcrum is a boxcutter
blade (highlighted in green). The inverted V is self-leveling if there is
nothing attached to it. This means that under load, there is a small restoring
torque unless the arm is level. In this picture you can also see the thin
wire that comes up rom the small sphere, and connects it to ground.
coming up from the sphere
The measurement procedure is as follows:
| |
Measurements: I untied and retied the counterweight a bunch of times at
different heights,
distance between scale the spheres (mm) reading ------------------------- 77 spark at 20g 116 spark at 16g 84 12g 147 10g 184 9g 184 7g 159 9g 95 17g 62 spark - 85 spark - 119(?) 17g -------------------------Ambient conditions on 28 Dec 2014: 32°F, 33% relative humidity, sunny, no wind. Big sphere: 11" diameter → R1 = 14 cm. Small sphere 38 cm circumference → R2 = 6.0 cm. plot script | |
What voltage would cause this force? I found some papers that contain expressions for this:
1) Cruz and Ley-Koo: Evaluation and measurement of forces between two conducting spheres This paper had calculations as well as measurements. I overlayed plots for different ratios between sphere radii. Our spheres have a ratio of 0.43, which turns out to be a very large extrapolation from the published curves. | |
The authors very kindly ran their code to produce a new curve corresponding to spheres of 1.775 and 0.76 cm, which is the same ratio as my spheres. In blue is plotted a subset of the new points. | |
and
and
and
and
and Electrostatic force between two conducting spheres at constant potential difference | xxx |